Monte Carlo Simulations of the Quantum X-Y Model by a Loop-Cluster Algorithm

The quantum X-Y model of interacting spins on square lattices is simulated by a loop-cluster algorithm.It is shown that the method can be used to simulate the systems efficiently at low temperatures for lattices as large as 32×32×200.

Electrical Conductivity of the Two-Dimensional Half-Filled Hubbard Model

The electrical conductivity of the one-band Hubbard model on a two-dimensional square lattice at half-filling is studied through the grand canonical quantum Monte Calro method.Our results support that there exists an insulator-to-metal transition for the half-filled Hubbard model at high temperature.

On the Order of the Phase transition in the Three-State Vector Potts Model on a Two-Dimensional Random Lattice

We performed a Monte Carlo simulation of the three-state(Q=3)vector Potts model on a 2-D random lattice.It is shown that there is a peak in the specific heat but no thermal hysterisis of the energy that corresponds to a high-order phase transition(a second-order one).The result agrees with the analytical calculation and the qualitative picture obtained for the same model on the square lattice.

MONTE CARLO STUDY OF SU(2)×SU(2) CHIRAL MODEL WITH MIXED ACTION ON THE 2-DIMENSIONAL RANDOM LATTICE

We analyzed the SU(2)×SU(2)chiral model with mixed fundamental-adjoint action on the 2-dimensional(2-D)random lattice by using Monte-Carlo(M-C)simulation.The results sluw that the model behaves like the mixed SU(2)×SU(2)chiral model on the 2-D regular lattice,but the character of the phase transition seems to be different.

MONTE CARLO SIMULATION OF SU(3)xSU(3)CHIRAL MODEL ON A 2-DIMENSIONAL RANDOM LATTICE

Monte Carlo(M-C)measurements of the SU(3)xSU(3)chiral model defined on a N×N 2-dimensional(2-D)random lattice are presented.Calculations are made of energy,specific heat and order parameter per spin on the 10×10,12×12 and 16×16 lattics.It is shown that the system enters a crossover region at β=4.75±0.10,but no evidences of phase transition are obtained.It is found that our results are consistent with that of the 4-D gauge theory and the 2-D chiral model on the regular lattice.

Channel noise-induced phase transition of spiral wave in networks of Hodgkin-Huxley neurons

The phase transition of spiral waves in networks of Hodgkin-Huxley neurons induced by channel noise is investigated in detail.All neurons in the networks are coupled with small-world connections,and the results are compared with the case for regular networks,in which all neurons are completely coupled with nearest-neighbor connections.A statistical variable is defined to study the collective behavior and phase transition of the spiral wave due to the channel noise and topology of the network.The effect of small-world connection networks is described by local regular networks and long-range connection with certain probability p.The numerical results confirm that (1) a stable rotating spiral wave can be developed and maintain robust with low p,where the breakup of the spiral wave and turbulence result from increasing the probability p to a certain threshold;(2) appropriate intensity of the optimized channel noise can develop a spiral wave among turbulent states in small-world connection networks of H-H neurons;and (3) regular connection networks are more robust to channel noise than small-world connection networks.A spiral wave in a small-world network encounters instability more easily as the membrane temperature is increased to a certain high threshold.

Detecting the breakup of spiral waves in small-world networks of neurons due to channel block

The breakup of a spiral wave by blockade of sodium and potassium channels in a small-world network of Hodgkin-Huxley neurons is investigated in detail.The influence of ion channel block in poisoned excitable membrane patches of a certain size is measured,by varying channel noise and channel densities resulting from the change in conductance,For example,tetraethylammonium is known to cause a block(poisoning) of potassium channels,while tetrodotoxin blocks sodium channels.We observed the occurrence of spiral waves,which are ordered waves believed to play an important role in facilitating the propagation of electric signals across quiescent regions of the brain.In this paper,the effect of channel block was measured by the factors xK and xNa,which represent the ratios of unblocked,or active,ion channels,to the overall number of potassium or sodium ion channels,respectively.To quantify these observations,we use a simple but robust synchronization measure,which succinctly captures the transition from spiral waves to other collective states,such as broken segments resulting from the breakup of the spiral wave.The critical thresholds of channel block can be inferred from the abrupt changes occurring in plots of the synchronization measure against different values of xK and xNa.Notably,small synchronization factors can be tightly associated with states where the formation of spiral waves is robust to mild channel block.

Emergence of target waves in neuronal networks due to diverse forcing currents

The electric activities of neurons could be changed when ion channel block occurs in the neurons.External forcing currents with diversity are imposed on the regular network of Hodgkin-Huxley(HH) neuron,and target waves are induced to occupy the network.The forcing current I1 is imposed on neurons in a local region with m 0 ×m 0 nodes in the network,neurons in other nodes are imposed with another forcing current I2.Target wave could be developed to occupy the network when the gradient forcing current(I1-I2) exceeds certain threshold,and the formation of target wave is independent of the selection of boundary condition.It is also found that the developed target wave can decrease the negative effect of ion channel block and suppress the spiral wave,and thus channel noise is also considered.The potential mechanism of formation of target wave could be that the gradient forcing current(I1-I2) generates quasi-periodical signal in local area,and the propagation of quasi-periodical signal induces target-like wave due to mutual coupling among neurons in the network.